/// \file
/// \ingroup tutorial_roostats
/// \notebook -js
/// Example of the BernsteinCorrection utility in RooStats.
///
/// The idea is that one has a distribution coming either from data or Monte Carlo
/// (called "reality" in the macro) and a nominal model that is not sufficiently
/// flexible to take into account the real distribution.  One wants to take into
/// account the systematic associated with this imperfect modeling by augmenting
/// the nominal model with some correction term (in this case a polynomial).
/// The BernsteinCorrection utility will import into your workspace a corrected model
/// given by nominal(x) * poly_N(x), where poly_N is an n-th order polynomial in
/// the Bernstein basis.  The degree N of the polynomial is chosen by specifying the tolerance
/// one has in adding an extra term to the polynomial.
/// The Bernstein basis is nice because it only has positive-definite terms
/// and works well with PDFs.
/// Finally, the macro makes a plot of:
///  - the data (drawn from 'reality'),
///  - the best fit of the nominal model (blue)
///  - and the best fit corrected model.
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Kyle Cranmer

#include "RooDataSet.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooBernstein.h"
#include "TCanvas.h"
#include "RooAbsPdf.h"
#include "RooFitResult.h"
#include "RooPlot.h"
#include <string>
#include <vector>
#include <stdio.h>
#include <sstream>
#include <iostream>

#include "RooProdPdf.h"
#include "RooAddPdf.h"
#include "RooGaussian.h"
#include "RooProfileLL.h"
#include "RooWorkspace.h"

#include "RooStats/BernsteinCorrection.h"

// use this order for safety on library loading
using namespace RooFit;
using namespace RooStats;

//____________________________________
void rs_bernsteinCorrection()
{

   // set range of observable
   Double_t lowRange = -1, highRange = 5;

   // make a RooRealVar for the observable
   RooRealVar x("x", "x", lowRange, highRange);

   // true model
   RooGaussian narrow("narrow", "", x, RooConst(0.), RooConst(.8));
   RooGaussian wide("wide", "", x, RooConst(0.), RooConst(2.));
   RooAddPdf reality("reality", "", RooArgList(narrow, wide), RooConst(0.8));

   RooDataSet *data = reality.generate(x, 1000);

   // nominal model
   RooRealVar sigma("sigma", "", 1., 0, 10);
   RooGaussian nominal("nominal", "", x, RooConst(0.), sigma);

   RooWorkspace *wks = new RooWorkspace("myWorksspace");

   wks->import(*data, Rename("data"));
   wks->import(nominal);

   if (TClass::GetClass("ROOT::Minuit2::Minuit2Minimizer")) {
      // use Minuit2 if ROOT was built with support for it:
      ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2");
   }

   // The tolerance sets the probability to add an unnecessary term.
   // lower tolerance will add fewer terms, while higher tolerance
   // will add more terms and provide a more flexible function.
   Double_t tolerance = 0.05;
   BernsteinCorrection bernsteinCorrection(tolerance);
   Int_t degree = bernsteinCorrection.ImportCorrectedPdf(wks, "nominal", "x", "data");

   if (degree < 0) {
      Error("rs_bernsteinCorrection", "Bernstein correction failed ! ");
      return;
   }

   cout << " Correction based on Bernstein Poly of degree " << degree << endl;

   RooPlot *frame = x.frame();
   data->plotOn(frame);
   // plot the best fit nominal model in blue
    nominal.fitTo(*data, PrintLevel(0));
   nominal.plotOn(frame);

   // plot the best fit corrected model in red
   RooAbsPdf *corrected = wks->pdf("corrected");
   if (!corrected)
      return;

   // fit corrected model
   corrected->fitTo(*data, PrintLevel(0));
   corrected->plotOn(frame, LineColor(kRed));

   // plot the correction term (* norm constant) in dashed green
   // should make norm constant just be 1, not depend on binning of data
   RooAbsPdf *poly = wks->pdf("poly");
   if (poly)
      poly->plotOn(frame, LineColor(kGreen), LineStyle(kDashed));

   // this is a switch to check the sampling distribution
   // of -2 log LR for two comparisons:
   // the first is for n-1 vs. n degree polynomial corrections
   // the second is for n vs. n+1 degree polynomial corrections
   // Here we choose n to be the one chosen by the tolerance
   // criterion above, eg. n = "degree" in the code.
   // Setting this to true is takes about 10 min.
   bool checkSamplingDist = true;
   int numToyMC = 20; // increase this value for sensible results

   TCanvas *c1 = new TCanvas();
   if (checkSamplingDist) {
      c1->Divide(1, 2);
      c1->cd(1);
   }
   frame->Draw();
   gPad->Update();

   if (checkSamplingDist) {
      // check sampling dist
      ROOT::Math::MinimizerOptions::SetDefaultPrintLevel(-1);
      TH1F *samplingDist = new TH1F("samplingDist", "", 20, 0, 10);
      TH1F *samplingDistExtra = new TH1F("samplingDistExtra", "", 20, 0, 10);
      bernsteinCorrection.CreateQSamplingDist(wks, "nominal", "x", "data", samplingDist, samplingDistExtra, degree,
                                              numToyMC);

      c1->cd(2);
      samplingDistExtra->SetLineColor(kRed);
      samplingDistExtra->Draw();
      samplingDist->Draw("same");
   }
}
